Problem: Mindy and Troy combined ate $9$ pieces of the wedding cake. Mindy ate $3$ pieces of cake and Troy had $\dfrac14$ of the total cake. Write an equation to determine how many pieces of cake $(c)$ there were in total. Find the total number of pieces of cake.
Answer: Let $c$ be the total number of pieces of wedding cake. Mindy had $3$ pieces of cake. Troy ate $\dfrac14$ of the cake, which is equal to $\dfrac14c$. Mindy and Troy combined to eat $3+\dfrac14c$ pieces of cake. Since they ate $9$ pieces of cake, let's set this equal to $9$ : $ 3+\dfrac14c=9$ Now, let's solve the equation to find the total number of pieces of wedding cake $(c)$. $\begin{aligned} 3+\dfrac14c&=9\\ \\ 3+\dfrac14c{-3}&=9{-3}&&{\text{subtract }3} \text{ from each side}\\ \\ \dfrac14c&=6\\ \\ \dfrac{\dfrac14c}{{\dfrac14}}&=\dfrac{6}{{\dfrac14}}&&\text{divide each side by ${\dfrac14}$}\\ \\ c&=24\end{aligned}$ The equation is $3+\dfrac14c=9$. There were a total of $24$ pieces of cake.